Half the perimeter of a rectangular garden, whose length is $4 m$ more than its width is $36 m$. Find the dimension of the garden.

Solve simultaneous linear equations in two variables by the method of elimination.

$41x+53y=135, 53x+41y=147$

Solve simultaneous linear equations in two variables by the method of elimination.

$\frac{x}{2}+\frac{y}{3}=2, \frac{x}{4}+\frac{y}{2}=2$

Solve the following system of equations in $x$ and $y$:

$(a-b)x+(a+b)y=a^2-2ab-b^2, (a+b)(x+y)=a^2+b^2$
 

Solve the following simultaneous equations.

$99 x+101 y=499 ; 101 x+99 y=501$